Unit Plan 21 (Grade 8 Math): Dilations & Similarity
8th graders explore dilations and similarity, using centers and scale factors to model how figures resize while preserving angles and parallel lines. They apply coordinate rules, verify properties, and prove similarity through transformation sequences.
Focus: Explore dilations from a center, scale factor effects on coordinates, and similarity via transformations.
Grade Level: 8
Subject Area: Mathematics (Geometry)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week students meet dilations—transformations that resize figures from a center by a scale factor k (k > 0). They’ll use coordinates to perform dilations, predict images, and verify what changes and what stays the same: angles stay the same, lengths scale by k, parallel lines remain parallel, and orientation is preserved. Then they’ll formalize similarity: one figure is similar to another if a sequence of transformations (dilations and/or rigid motions) maps one onto the other.
Essential Questions
- How does a dilation from a given center with scale factor k change coordinates and measurements?
- Which properties are preserved under dilation (angles, parallelism, orientation), and which change (lengths, area)?
- How can I prove two figures are similar by describing a precise transformation sequence?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Perform and describe dilations on the coordinate plane from the origin and from other centers; write coordinate rules and track images of key points.
- Explain and verify what dilations preserve (angles, parallelism, orientation) and what they scale (lengths by k; area by k squared).
- Determine whether two figures are similar by exhibiting a sequence of dilations and rigid motions; identify the scale factor and corresponding parts.
- Communicate solutions with precise language (center, scale factor, vector, line of reflection, rotation angle) and clean diagrams.
Standards Alignment — CCSS Grade 8
- 8.G.3: Describe the effect of dilations, translations, rotations, and reflections on 2D figures using coordinates.
- 8.G.4: Understand that two 2D figures are similar if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations; given two similar figures, describe a sequence that exhibits the similarity.
Success Criteria (student-friendly)
- I can apply a dilation rule and find the image of any point relative to a named center and k.
- I can state which properties are preserved and which are scaled, and show evidence.
- I can decide similar/not and, if similar, give a specific sequence (order matters) with the scale factor.
- I can label corresponding parts and use clear, concise transformation vocabulary.